Grothendieck's theory of motives

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:logic
gptkbp:aimsTo	unify cohomology theories
gptkbp:category	gptkb:Tannakian_category abelian category triangulated category
gptkbp:developedFurtherBy	gptkb:Yves_André gptkb:Pierre_Deligne gptkb:Vladimir_Voevodsky
gptkbp:field	gptkb:algebraic_geometry
gptkbp:hasConcept	motive category of motives mixed motives morphisms of motives pure motives
https://www.w3.org/2000/01/rdf-schema#label	Grothendieck's theory of motives
gptkbp:influenced	gptkb:motivic_integration modern algebraic geometry motivic cohomology the theory of motives over finite fields
gptkbp:introducedIn	1960s
gptkbp:proposedBy	gptkb:Alexander_Grothendieck
gptkbp:relatedTo	gptkb:Hodge_conjecture gptkb:Tate_conjecture gptkb:category_theory gptkb:motivic_Eilenberg–MacLane_spectrum gptkb:motivic_Galois_group gptkb:motivic_L-functions gptkb:motivic_Steenrod_algebra gptkb:motivic_fundamental_group gptkb:motivic_homotopy_theory gptkb:motivic_integration gptkb:motivic_sheaves gptkb:motivic_stable_homotopy_category gptkb:Weil_cohomology_theories gptkb:motivic_Adams_spectral_sequence gptkb:motivic_Donaldson–Thomas_invariants gptkb:motivic_Milnor_fiber gptkb:motivic_polylogarithms gptkb:standard_conjectures_on_algebraic_cycles algebraic cycles motivic cohomology motivic cohomology operations motivic nearby cycles motivic fundamental group scheme motivic measures motivic periods motivic vanishing cycles motivic zeta functions
gptkbp:bfsParent	gptkb:Alexander_Grothendieck
gptkbp:bfsLayer	5